Question

if ∆ABC and ∆PQR and AB:PQ = 3:4, write the ratio of area of ∆ABC and ∆PQR....

Answer 1

if Triangle ABC And PQR are similar then ratio of their areas is equal to the square of the ratio of their corresponding side.
that means area of ABC : area of PQR = AB ^2 : PQ ^2
=3^2:4^2=9:16
the answer is 9:16.

Answer 2

Answer:

We have been asked to find the ratio of areas of two triangle whose ratio of sides are given.

Step-by-step explanation:

Given: Two triangles ΔABC and ΔPQR, ratio of whose sides AB and PQ are 3:4.

To Find: ratio of areas of ΔABC and ΔPQR.

Now, let us proceed towards the question.

As the sides of the triangles can be represented with respect to each other in ratios, the triangles are similar. This means, their sides and areas can be calculated with the help of each other by some relations.

If two triangles, ΔXYZ and ΔLMN are similar, this means their all sides are in same ratio with each other.

That is, XY : LM = YZ : MN = XZ : LN.

Now, from one of the theorems in similarities of triangles, we can find the relation between ratio of areas to ratio of sides and it is:

Ratio of areas of two similar triangles = (Ratio of sides of triangles)²

Hence, we can easily calculate our answer, given that ratio sides are already mentioned in the question.

Hence, ΔABC : ΔPQR = (AB : PQ)²

                                    = (3 : 4)²

           ΔABC : ΔPQR = 9 : 16

Therefore, ratio of areas of ΔABC and ΔPQR is 9 : 16.